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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Figueiredo, Isabel N. Leal, Carlos Romanazzi, Giuseppe and Engquist, Bjorn 2016. Homogenization Model for Aberrant Crypt Foci. SIAM Journal on Applied Mathematics, Vol. 76, Issue. 3, p. 1152.
    Figueiredo, Isabel N. Romanazzi, Giuseppe Leal, Carlos and Engquist, Bjorn 2013. A Multiscale Model for Aberrant Crypt Foci. Procedia Computer Science, Vol. 18, Issue. , p. 1026.
    Figueiredo, Isabel N. and Leal, Carlos 2013. Physiologic Parameter Estimation Using Inverse Problems. SIAM Journal on Applied Mathematics, Vol. 73, Issue. 3, p. 1164.
    Pham, K. Frieboes, H. B. Cristini, V. and Lowengrub, J. 2011. Predictions of tumour morphological stability and evaluation against experimental observations. Journal of The Royal Society Interface, Vol. 8, Issue. 54, p. 16.
    Osborne, J. M. O’Dea, R. D. Whiteley, J. P. Byrne, H. M. and Waters, S. L. 2010. The Influence of Bioreactor Geometry and the Mechanical Environment on Engineered Tissues. Journal of Biomechanical Engineering, Vol. 132, Issue. 5, p. 051006.
    Byrne, Helen and Drasdo, Dirk 2009. Individual-based and continuum models of growing cell populations: a comparison. Journal of Mathematical Biology, Vol. 58, Issue. 4-5, p. 657.
    Franks, S.J. and King, J.R. 2009. Interactions between a uniformly proliferating tumour and its surroundings: Stability analysis for variable material properties. International Journal of Engineering Science, Vol. 47, Issue. 11-12, p. 1182.
    O'DEA, R. D. WATERS, S. L. and BYRNE, H. M. 2008. A two-fluid model for tissue growth within a dynamic flow environment. European Journal of Applied Mathematics, Vol. 19, Issue. 06, p. 607.
    Lemon, G. and King, J. R. 2007. Travelling-wave behaviour in a multiphase model of a population of cells in an artificial scaffold. Journal of Mathematical Biology, Vol. 55, Issue. 4, p. 449.
    WILSON, DUNCAN J. KING, JOHN R. and BYRNE, HELEN M. 2007. MODELLING SCAFFOLD OCCUPATION BY A GROWING, NUTRIENT-RICH TISSUE. Mathematical Models and Methods in Applied Sciences, Vol. 17, Issue. supp01, p. 1721.
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Mathematical analysis of some multi-dimensional tissue-growth models

  • J. R. KING (a1) and S. J. FRANKS (a1)
Abstract

Mathematical models for the growth of nutrient-rich tissue are presented and a number of properties of the resulting models outlined. The focus is on obtaining broadly applicable results for the simplest appropriate formulations by using matched-asymptotic, moving-boundary and thin-film approaches; the relevance of the results to a variety of specific biological applications will be addressed elsewhere, as will the inclusion of additional physical phenomena.

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2004 Cambridge University Press
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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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